© K. Douka,  T. Higham, E. Mastora

BAYESIAN MODELLING 

The application of Bayesian statistics is probably the single biggest development in chronology building over the past 20 years and a key part of the PalaeoChron dating approach.

 

INTCAL13, the most recently published internationally-agreed radiocarbon calibration curve, extends back to 50,000 cal BP, but single calibrated ages result in wide probability distributions that are often only coarsely useful. Bayesian modelling and the construction of robust probabilistic frameworks help us address questions that presently are not possible to answer due to dating imprecision.

Bayesian modelling allows radiocarbon data to be analysed along with relative archaeological information ("prior information", e.g. stratigraphic and contextual details, material-related uncertainties) in a formal statistical approach. This can :

 

a) generate formal date estimates that are often much more precise than single calibrations and;

b) provide robust probability distributions for specific boundary events within the constructed models.

 

The boundaries are estimated probabilities which usually correspond to the beginning and ending of archaeological phases, and therefore are crucially important in inter-site and interregional comparisons. In addition, the application of Bayesian methods  enables us to combine dates from different techniques into one chronometric model.

An example of how Bayesian modelling works: a series of calibrated radiocarbon ages is shown in grey. The same series was incorporated into a Bayesian framework where additional (prior) information as to the relative position of each determination to the other was added. The generated probabilities, i.e. the posterior density estimates, are shown in green. In red, are the estimated probabilities for the start and the beginning of the given phase.

 

We use the OxCal software, developed by Prof. C. Bronk Ramsey, Co-Investigator in the project, to calibrate our results and generate Bayesian models. OxCal also allows comparisons of the resulting chronologies against palaeoenvironmental proxies.

Abri Pataud (Dordogne, France)

Case Study

 

We have applied Bayesian statistics for refining the chronology of several Palaeolithic sites in recent years. The site of Abri Pataud (France) is a good example (pictured below).

 

A new series of ultrafiltered AMS dates produced a much greater consistency than the old determinations. The dated samples were cut-marked or humanly modified bones and artefacts from discrete, well-excavated archaeological levels, separated from one another by sterile layers. Sedimentological and micro-morphological analysis during and after excavation has shown virtually no movement of material between layers, therefore the site lends itself to Bayesian modelling in which  prior information are the superposed horizons.

 

The model to the right (after Higham et al., 2011) shows the calibrated likelihoods given in phases (= archaeological layers) from the lowest (Niveau 14 – the early Aurignacian) to uppermost (Niveau 5 – the early Gravettian).

 

Boundaries constrain each phase and provide additional information, which allow us to measure the start and end dates of different archaeological and lithostratigraphic phases. In addition, this approach gives us the opportunity to examine the climatic backdrop at the time of the occupation of sites like Abri Pataud, and compare the results with the archaeological evidence, for example the faunal record from the site.

 

The Bayesian modelling for layers 14-5 of Abri Pataud (after Higham et al. 2011)